Lattices from Codes

Sueli I.R. Costa; Frédérique Oggier; Antonio Campello; Jean Claude Belfiore; Emanuele Viterbo

doi:10.1007/978-3-319-67882-5_3

Lattices from Codes

Sueli I.R. Costa^*, Frédérique Oggier, Antonio Campello, Jean Claude Belfiore, Emanuele Viterbo

^*Corresponding author for this work

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

A natural way of constructing lattices is from error-correcting codes, using the so-called Construction A. It associates a lattice in ℝⁿ to a linear code in ℤqn (the set ℤ_q of integers modulo q will be introduced next). Such lattices are also called q-ary lattices (or modulo-q lattices) and have several applications in information theory and cryptography.

Original language	English
Title of host publication	SpringerBriefs in Mathematics
Publisher	Springer Science and Business Media B.V.
Pages	37-58
Number of pages	22
DOIs	https://doi.org/10.1007/978-3-319-67882-5_3
Publication status	Published - 2017

Publication series

Name	SpringerBriefs in Mathematics
ISSN (Print)	2191-8198
ISSN (Electronic)	2191-8201

Bibliographical note

Publisher Copyright:
© 2017, The Author(s).

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-319-67882-5_3

Cite this

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AU - Campello, Antonio

AU - Belfiore, Jean Claude

AU - Viterbo, Emanuele

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Y1 - 2017

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AB - A natural way of constructing lattices is from error-correcting codes, using the so-called Construction A. It associates a lattice in ℝn to a linear code in ℤqn (the set ℤq of integers modulo q will be introduced next). Such lattices are also called q-ary lattices (or modulo-q lattices) and have several applications in information theory and cryptography.

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Lattices from Codes

Abstract

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Bibliographical note

ASJC Scopus subject areas

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